Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 46.28   b = 19.43   c = 42

Area: T = 408.0329992473
Perimeter: p = 107.71
Semiperimeter: s = 53.855

Angle ∠ A = α = 90.01110054573° = 90°40″ = 1.57109884083 rad
Angle ∠ B = β = 24.82442196803° = 24°49'27″ = 0.43332643677 rad
Angle ∠ C = γ = 65.16547748624° = 65°9'53″ = 1.13773398777 rad

Height: ha = 17.63331025269
Height: hb = 421.9999992252
Height: hc = 19.43299996416

Median: ma = 23.13766127599
Median: mb = 43.11107640271
Median: mc = 28.61326134773

Inradius: r = 7.57664551569
Circumradius: R = 23.14400004269

Vertex coordinates: A[42; 0] B[0; 0] C[42.00437321429; 19.43299996416]
Centroid: CG[28.00112440476; 6.47766665472]
Coordinates of the circumscribed circle: U[21; 9.719903389]
Coordinates of the inscribed circle: I[34.425; 7.57664551569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.98989945427° = 89°59'20″ = 1.57109884083 rad
∠ B' = β' = 155.176578032° = 155°10'33″ = 0.43332643677 rad
∠ C' = γ' = 114.8355225138° = 114°50'7″ = 1.13773398777 rad

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How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 46.28+19.43+42 = 107.71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 107.71 }{ 2 } = 53.86 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.86 * (53.86-46.28)(53.86-19.43)(53.86-42) } ; ; T = sqrt{ 166488.47 } = 408.03 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 408.03 }{ 46.28 } = 17.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 408.03 }{ 19.43 } = 42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 408.03 }{ 42 } = 19.43 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 19.43**2+42**2-46.28**2 }{ 2 * 19.43 * 42 } ) = 90° 40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 46.28**2+42**2-19.43**2 }{ 2 * 46.28 * 42 } ) = 24° 49'27" ; ; gamma = 180° - alpha - beta = 180° - 90° 40" - 24° 49'27" = 65° 9'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 408.03 }{ 53.86 } = 7.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 46.28 }{ 2 * sin 90° 40" } = 23.14 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.43**2+2 * 42**2 - 46.28**2 } }{ 2 } = 23.137 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 46.28**2 - 19.43**2 } }{ 2 } = 43.111 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.43**2+2 * 46.28**2 - 42**2 } }{ 2 } = 28.613 ; ;
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